Math fact:

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Math fact For very large and very small
numbers, mega- indicated 106, giga - indicated
109, micro -indicates 10-6, nano -indicated 10-9,
and pico -indicated 10-12
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Vocabulary
Scientific Notation a way to express numbers
that are very large or very small Example Expres
sed as 2 factors 3x103
3(10)(10)(10) 3,000
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The table shows relationships between several
powers of 10.

• Each time you divide by 10, the exponent in the
  power decreases by 1 and the decimal point in the
  value moves one place to the left.

• Each time you multiply by 10, the exponent in the
  power increases by 1 and the decimal point in the
  value moves one place to the right.

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You can find the product of a number and a power
of 10 by moving the decimal point of the number.
You may need to write zeros to the right or left
of the number in order to move the decimal point.
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Examples Multiplying by Powers of Ten
Multiply.
1A. 14 ? 104
Since the exponent is a positive 4, move the
decimal point 4 places to the right.
14.0 0 0 0
140,000
1B. 3.6 ? 10-5
Since the exponent is a negative 5, move the
decimal point 5 places to the left.
0 0 0 0 3.6
0.000036
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Powers of 10 are used when writing numbers in
scientific notation. Scientific notation is a way
to express numbers that are very large or very
small. Numbers written in scientific notation are
expressed as 2 factors. One factor is a number
greater than or equal to 1. The other factor is a
power of 10.
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Examples Writing Numbers in Scientific Notation
Write the number in scientific notation.
2A. 0.00709
Think The decimal needs to move 3 places to get
a number between 1 and 10.
Think The number is less than 1, so the exponent
will be negative.
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Example Writing Numbers in Scientific Notation
Write the number in scientific notation.
2B. 23,000,000,000
Think The decimal needs to move 10 places to get
a number between 1 and 10.
Think The number is greater than 1, so the
exponent will be positive.
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Example Reading Numbers in Scientific Notation
Write the number in standard form.
3A. 1.35 ? 105
Think Move the decimal right 5 places.
1.35000
135,000
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Example Reading Numbers in Scientific Notation
Write the number in standard form.
3B. 2.7 ? 103
Think Move the decimal left 3 places.
0002.7
0.0027
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Talking Example 4 Comparing Numbers in
Scientific Notation
A certain cell has a diameter of approximately
4.11 ? 10-5 meters. A second cell has a diameter
of 1.5 ? 10-5 meters. Which cell has a greater
diameter?
4.11 ? 10-5 1.5 ? 10-5
Compare the exponents.
Compare the values between 1 and 10.
4.11 gt 1.5
Notice that 4.11 ? 10-5 gt 1.5 ? 10-5.
The first cell has a greater diameter.
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Check It Out! Examples
Multiply.
A. 2.5 ? 105
Since the exponent is a positive 5, move the
decimal point 5 places to the right.
2.5 0 0 0 0
250,000
B. 10.2 ? 10-3
Since the exponent is a negative 3, move the
decimal point 3 places to the left.
0 10.2
0.0102
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Check It Out! Examples
Write the number in scientific notation.
A. 0.000811
Think The decimal needs to move 4 places to get
a number between 1 and 10.
Think The number is less than 1, so the exponent
will be negative.
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Check It Out! Example
Write the number in standard form.
A. 2.87 ? 109
Think Move the decimal right 9 places.
2.870000000
2,870,000,000
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Check It Out! Example
Write the number in standard form.
B. 1.9 ? 105
000001.9
Think Move the decimal left 5 places.
0.000019
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Check It Out! Example 4
A star has a diameter of approximately 5.11 ?
103 kilometers. A second star has a diameter of 5
? 104 kilometers. Which star has a greater
diameter?
5.11 ? 103 5 ? 104
Compare the exponents.
Notice that 3 lt 4. So 5.11 ? 103 lt 5 ? 104
The second star has a greater diameter.
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Check It Out! Example 2
Write the number in scientific notation.
B. 480,000,000
Think The decimal needs to move 8 places to get
a number between 1 and 10.
Think The number is greater than 1, so the
exponent will be positive.